# Parametric and non-parametric tests

What is the difference between parametric and non-parametric statistics, their purpose and applications in biological sciences?

Question

What is the difference between parametric and non-parametric statistics, their purpose and applications in biological sciences?

- Regarding the test used in statistics (whether parametric or non-parametric, i.e., normally distributed population) you have to consider the followings; I mean before you can decide which one is best suited to your particular analysis, you have to be clear about the following:

a. whether you wish to make decisions about differences between the populations from which your samples come, or whether you wish to make decisions about associations between features wthin the population from which your sample come.

b. whether your measurements are at the interval, ordinal or categorical level

C. whether your measurements are matched or unmatched

Once you are certain about these things, you might use the appropraite test according to the rationale of test. Indeed, all the statistical techniques have both advantages and disadvantages, and it is up to you to weigh them up in the context of your own project.

Non-parametric tests are ones that test hypotheses which do not make assumpations about the population parameters, while distribution free tests do not make assumptions about the population distribution. Thy have the advantage that they can applied in more general conditions than can parametric tests. The sample sizes are also playing a role in choosing the test. - Thanks Sherif for posting comprehensive explanation regarding parametric and non-parametric statistics
- As I mentioned above, I agree with Borotkanics that, in general, the difference is between normal distribution for parametric tests and not normally distribution for nonparametric tests. The sample size is also play a role is that if small number nonparametric test is used. Since with large number of sample, will be more normally distributed and variation will be less and parametric tests could be used. Thus, sample size and normal distribution of data are major factors.
- It is important to stress that inferential testing has to do with sample and not population variance, in other words it has to do with the variability of sample means and not of the actual statistical units. sample variance in any case becomes normal (whatsoever the shape of the population distribution) at N=30 with N= numerosity of the sample. Thus the choice of non-parametric test instead of a parametric one is driven by the need of depotentiating the effect of outliers and, more in genral, of the uncertainty of measures.
- Thanks Sherif, Giuliani and Robert

for useful comments - Parametric tests test model parameters (a model may model the effect of a treatment on some physiological response), non-parametric tests test the difference distributions. A parametric test can give you a result like "it is very unecpected to observe at leat such strong effects if the samples were taken from the same population". A non-parametric test can give you a result like "it is very unexpected to observe at leat such a big difference in the distributions if the samples were taken from the same distribution". Which test to use depends on the question you want to answer.

Very often, the t-test is compared to its non-parametric alternative (Mann-Whitney/Wilcoxon test). Notably, the latter compares distributions, i.e., it is sensitive to whole bunch of distributional properties. This test can be used to specifically test a location shift ONLY when ALL OTHER distributional properties are identical. This is often overseen. Many papers show results of a MW/W-test to test a location shift on data with clearly different variances between the groups. In this case, the test result does not specifically represent the location shift. I would be required to transform the data. But often, for the transformed data there is a reasonable model for which again the parameters can be tested directly... - Parametric methods deal with the estimation of population parameters (like the mean)

while the non-parametric are distribution free methods. They rely on ordering (ranking) of observations.

.

More specifically, the data distribution is significant in the choice between parametric and non-parametric procedures.If we believe that the populations are normally distributed then we use parametric methods. If we are not sure or we suspect that they do not behave normally then we use non-parametric methods.

Similarly the scale of the data is important. That is categorical (nominal) or ordinal scale data demand the use of non-parametric methods while in the case of interval and ratio scale data where we cannot assume population normality then again non-parametric methods have to be used.

As an example ANOVA is a parametric method while Kruskal Wallis is the corresponding non-parametric method which has to be used in case the assumption of normality is rejected in the before the use of ANOVA tests (equality of variances with Bartlett's test and normality with Kolmogorov-Smirnov test).

Similarly the Mann-Whitney in non-parametric corresponds to the pooled t test in parametrics. The paired t test in parametrics to Wilcoxon signed rank test and in the case of one mean the Z, t tests in parametrics correspond to Wilcoxon signed test.

It is important to mention also the use of the non-parametric procedure of chi-square for testing frequencies in categories. Chi-square can be used for testing goodness of fit, independence and homogeneity. - parametric Information about population is completely known
- Null hypothesis is made on parameters of the population distribution
- it is very important to decide which test should be used for analysis. Parametric and non parametric test both test can be applied but it depends on some assumptions. most important assumption is normality of the data, its means that there is no outlier in the data that effect the mean of the outcome variable. if data is normally distributed then you can apply parametric tests that compare the means among the groups and if data is not normally distributed then you can apply non parametric test that compare the median among the groups.
- @Waqas: "parametric" does not neccesarily mean "normal". Parametric means to to specifically test the parameter of a well-defined model. This parameter can be a location parameter or any other parameter (slope, variance, some other "shape" parameter, a rate, ...). If a difference in means is to be tested, then the t-test is the only tool we have. This one requires symmetric and independent errors. If these assumptions are not fulfilled, we actually have no tool to test differences in means (except for bootstrap methods; see below). If a difference in rates or counts is to be tested, the available tools are Poisson- and negative binomial models. To test proportions we have binomial models. And so on! It is not about "normal or nothing".

Further, I do not know any "non-parametric" test that would specifically and generally test medians. Do you mean Wilcoxon/Mann-Whitney? This test compares rank distributions, not medians. It is especially sensitive to location shifts, that's right. But is well "detects" other differences in the rank distributions. This test is equivalent to a test of the medians ONLY when the shapes of the distributions are equal except the location (i.e. a plain shift towards higher or lower values, without changing the variance, skew, kurtosis and all other higher moments). And this test is typically recommended when the data are heteroscedastic, and just then it *won't* be a test of the medians. I can give you sample data to demonstrate that this test will give tiny p-values for samples with *identical* medians (but different means). I have never encountered a real-world example where a location-shift (without alterng the shape of the distribution) was the case. Usually, people simply do not recognize the correct model. In the biomed field it is often one of beta-, gamma-, Poisson-, or a log-normal model.

If medians are to be tested, I would recommend a bootstrap approach on the median.

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## Popular Answers

Deletedwhile the non-parametric are distribution free methods. They rely on ordering (ranking) of observations.

.

More specifically, the data distribution is significant in the choice between parametric and non-parametric procedures.If we believe that the populations are normally distributed then we use parametric methods. If we are not sure or we suspect that they do not behave normally then we use non-parametric methods.

Similarly the scale of the data is important. That is categorical (nominal) or ordinal scale data demand the use of non-parametric methods while in the case of interval and ratio scale data where we cannot assume population normality then again non-parametric methods have to be used.

As an example ANOVA is a parametric method while Kruskal Wallis is the corresponding non-parametric method which has to be used in case the assumption of normality is rejected in the before the use of ANOVA tests (equality of variances with Bartlett's test and normality with Kolmogorov-Smirnov test).

Similarly the Mann-Whitney in non-parametric corresponds to the pooled t test in parametrics. The paired t test in parametrics to Wilcoxon signed rank test and in the case of one mean the Z, t tests in parametrics correspond to Wilcoxon signed test.

It is important to mention also the use of the non-parametric procedure of chi-square for testing frequencies in categories. Chi-square can be used for testing goodness of fit, independence and homogeneity.

Fathi M Sherif· University of Tripolia. whether you wish to make decisions about differences between the populations from which your samples come, or whether you wish to make decisions about associations between features wthin the population from which your sample come.

b. whether your measurements are at the interval, ordinal or categorical level

C. whether your measurements are matched or unmatched

Once you are certain about these things, you might use the appropraite test according to the rationale of test. Indeed, all the statistical techniques have both advantages and disadvantages, and it is up to you to weigh them up in the context of your own project.

Non-parametric tests are ones that test hypotheses which do not make assumpations about the population parameters, while distribution free tests do not make assumptions about the population distribution. Thy have the advantage that they can applied in more general conditions than can parametric tests. The sample sizes are also playing a role in choosing the test.